The purpose of this essay is to describe a situation that we have found particularly exciting in our recent work in interior-point methods for linear programming. To our surprise, we have seen considerable theory developed ...

For linear programming, a primal-dual interior-point algorithm was recently constructed by Zhang and Tapia that achieves both polynomial complexity and Q-superlinear convergence (Q-quadratic in the nondegenerate case). In ...

In this paper, we introduce transformations that convert a large class of linear and/or nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over "orthants" of the form (R^n)++ × R^N, ...

In Part I of this series of papers, we have introduced transformations which convert a large class of linear and nonlinear semidefinite programs (SDPs) into nonlinear optimization problems over "orthants" of the form ...

A sequence of weighted linear least squares problems arises from interior-point methods for linear programming where the changes from one problem to the next are the weights and the right hand side. One approach for solving ...

In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) grad­f(x^k) for minimizing a function ...

This paper presents a convergence rate analysis for interior point primal-dual linear programming algorithms. Conditions that guarantee Q-superlinear convergence are identified in two distinct theories. Both state that, ...

In this paper, we extend the Q-superlinear convergence theory recently developed by Zhang, Tapia and Dennis for a class of interior point linear programming algorithms to similar interior point algorithms for quadratic ...

The choice of the centering (or barrier) parameter and the step length parameter are the fundamental issues in primal-dual interior-point algorithms for linear programming. Various choices for these two parameters have ...

The notion of the central path plays an important role in the convergence analysis of interior-point methods. Many interior-point algorithms have been developed based on the principle of following the central path, either ...